Low-density parity-check convolutional codes (LDPCCCs) achieve a better error performance than the LDPC block-code counterparts of similar decoding complexity. LDPCCCs have inherited the basic structure of convolutional codes therefore allowing continuous encoding and decoding of codes with variable length. This property has made LDPCCCs a promising technique in many applications.
Several parallelization concepts for the decoding process that lead to a high-throughput decoder architecture can achieve an information throughput of over 1 Gb/s with a clock frequency of 250 MHz. However, the decoder architecture is confined to time-invariant LDPCCCs and cannot be easily applied to time-varying codes which have a better error performance.
A register-based decoder architecture attaining up to 175 Mb/s throughput was proposed. The architecture successfully implements a pipeline decoder of ten processing units, but its register intensive architecture has limited its power efficiency. Later, a low-cost low-power memory-based decoder architecture that uses a single decoding processor was proposed. On one hand, the serial node operation uses a small portion of the field-programmable gate array (FPGA) resources. On the other hand, such a design has significant limitation on the achievable throughput. The memory-based design with parallel node operations have led to a substantial improvement on throughput. The high throughput under these designs, however, is achieved at the cost of a complicated shuffle/exchange-type switching network.
Previously proposed LDPCCC decoder architectures mainly handle random time-varying LDPCCCs. In recent literature, LDPCCCs of regular structures have attracted considerable interest. The construction of LDPCCC based on circulant matrices have been investigated. A lower bound of the free distance for unterminated protograph-based LDPCCC was analyzed and the free distance growth rates was shown to exceed the minimum distance growth rates of the corresponding LDPC block codes. Based on the free distance analysis, the average trapping set enumerators for the ensembles of protograph based LDPCCC was obtained. Later, it was observed that the decoding thresholds of asymptotically good irregular and regular LDPC codes formed by terminating the protograph based LDPCCC can approach the optimal maximum a posteriori (MAP) decoding thresholds of the corresponding LDPC block code ensembles on binary erasure channels (BEC) as the terminating length increases. The same observation is recently generalized to additive white Gaussian noise (AWGN) channels.